Dissertation Talk: Algebraic, Numerical, and Machine Learning Methods for Compiling to Fault-Tolerant Quantum Computers

Event details Date: Tuesday, August 4, 2026 Time: 10:00 AM to 10:00 AM Location: Soda 306 Type: Sports Audience: Faculty,Students About this event Quantum algorithms are written in terms of arbitrary unitary operations, but error-corrected quantum computers can only execute small sets of discrete instructions. Algorithms must be compiled into one of these restricted sets before they can run. On early fault-tolerant machines, where physical qubits are scarce and gate errors frequent, the quality of this compilation determines which computations are feasible. This dissertation develops compilation techniques from three domains: algebraic number theory, numerical methods, and machine learning. Algebraic methods represent gates exactly over rings of algebraic integers, yielding single-qubit synthesis with near-optimal gate counts and promising richer fault-tolerant gate sets as practical compilation targets. I introduce a novel integer-enumeration-based synthesis algorithm that compiles general single-qubit unitaries to the Clifford+√T gate set. This synthesizer produces circuits that pay less non-Clifford cost than their Clifford+T counterparts. Numerical methods leverage ideas from continuous optimization and linear algebra to synthesize multi-qubit unitaries that lack strict number-theoretic structure. The central technique is synthesis by diagonalization: rather than compiling a unitary outright, discrete search reduces it to a diagonal operator, allowing high-precision diagonal synthesis algorithms to capture the difficult non-Clifford components of wide unitaries. Machine learning methods decide how compiled operations are executed. I argue that early fault-tolerant computers will store logical qubits densely, leaving few qubits free for transporting information around the machine, and formulate gate scheduling on such devices as a sliding tile puzzle. Classical planners make dense machines practical, and planners based on neural Monte Carlo tree search find shorter schedules still. Together these methods span compilation from the synthesis... Official event details: https://events.berkeley.edu/eecs/event/324855-dissertation-talk-algebraic-numerical-and-machine